So through a single command, I can compute the SHA-256 hash of the downloaded ZIP file, and compare that to the checksum from the NOOBS downloads page (okay, okay, I still have to manually copy the checksum from the downloads page and paste it into the command line after the echo):

Note: I’m using “\” to indicate the line is too long for WordPress to display, but the command works just fine with the backslash in there. Here’s a screenshot in case you need further convincing (I ran it twice, once with and once without the backslash):

Voila! When the command line comes back with no output (as diff does when there are no differences between “files”), I know the checksum is good!